So, what indications are there that confirm that it is allegorical?
The difficulty here is that the text itself is the only evidence we have for making a judgement on that question.
The text is ancient, but clearly not as ancient as the events it purports to relate.
Its authorship and date of production is debatable and has been debated ever since it was regarded as Holy Scripture by Hebrew scholars and the early church. It is almost certainly not the work of a single individual and contains story elements which have been incorporated from other ancient legends and other religions, but the story as it now appears is uniquely Hebrew and establishes a view of God's creative supremacy in a radically distinctive manner which, in its time, was unusually monotheistic. It has a long history of being regarded as 'inspired' literature.
The two accounts of the creation contained in chapters 1:1-31 - 2:3, and 2:4-25, are quite distinct, different in a number of ways and linked by what appears to be an editorial addition. (Ch.2:4).
Both can be regarded as 'poetry' or 'prose' in genre but both are more appropriately categorised as 'mythic'. Here is the problem! the word 'myth' has a number of different meanings and the common one is now regarded as indicating something is 'untrue' or 'faked'. This is not the meaning intended when categorising Genesis ch. 1-5 as 'myth'.
Mythic literature is a technical theological term used to describe narrative which derives from Hebrew religion and culture and had probably a liturgical connotation.The Hebrew writers made use of myths not only in the first 11 chapters of Genesis, but elsewhere in the Bible as well.
In the first place though, I have to agree that it is true that myth is not history, that is, it is not, and does not profess to be, a record of events which happened at a particular place and at a particular time. But historical truth, as important as it is in its own way, is not the only kind of truth, and a myth can, and often does, represent a kind of truth which cannot be expressed in historical categories.
When we call the story of the fall, a myth, we don't deny its truth; we imply rather that its truth lies deeper than the kind of historical truth which rests on dates and documentary evidence. Hence, in order to get the term 'myth' in proper perspective we need to enquire into the origin and function of myths in the ancient civilisations which form the background of Hebrew religion and culture.
Not having any knowledge of that background, and treating the Genesis text as if it is an ancient newspaper report of current events is not only unlikely to reveal a true understanding of it, it is impossible to reach a correct conclusion as to its actual meaning. This is a serious problem for believers and non believers alike. Before a text can be either believed or rejected it has to be understood, and most people do not have the knowledge to do that. They have not studied ancient cultures and their motivations, but just assume they thought and wrote just as we do today. They did not. They thought very differently, wrote very differently and believed very differently from us today.
Now to answer your question in more detail:
Gen.Ch.2:4- ch.5, contains a number of 'themes' which appear in other ancient 'mythic' literature pre dating the Genesis narrative. Stories had a distinct function in Hebrew society, as in all other mid eastern civilisations. They were not primarily used to convey 'facts'. They were primarily used to unite people and produce a commonality of purpose and social cohesion.
Indications that confirm that it is allegorical.
(1) Nearly all ancient texts of this genre are allegorical and full of symbolism. They speak often of foundation events that no human being could have been an eye witness to. They are therefore 'revelational', not witness testimony.
(2) Man names the animals, (What other creature on earth has categorised species?) A. Only mankind.
(3) Rib is a poor translation from the Hebrew which actually meant a whole side. Indicating that woman and man are equally important to God and exist together as 'humanity' both created by God with God's nature and motivated by God's (Breath - Spirit). Also here a very early hint and warning that it is inappropriate for human beings to copulate with anything other than human beings.
Gen.2:20.
(4) The Hebrew play on words 'Adam', 'Eve', 'Woman', all having meanings in themselves apart from being the names of the characters in the story.
(5) Trees which have names and can 'magically' confer attributes such as 'knowledgeableness', 'life' etc.
(6) The serpent theme, which appears in many other ancient myths.
(7) The nakedness theme, indicating fear and vulnerability. A common nightmare scenario.
(8) The inclusion of so many archetypes. i.e. Toil, clothes, painful childbirth, fear, guilt, death, exclusion etc (All 'firsts', very appropriate for a genesis story), and all "Just So" explanations for the way things are now, in life as experienced today.
All very typical of the type of stories told within cultures to explain in simple, rememberably entertaining terms, important tribal customs and standards of acceptable behaviour.
Add then to all this that the narrative has survived millennia and the church believes it to be inspired by God, we should treat it with the respect it deserves and not merely take it at face value, either idolising or denigrating it by either insisting it is historical or rejecting it as nonsense.
Such black/white thoughtlessness is the epitome of ignorance.